AI 中文总结
本文刻画保持永久秩1矩阵的加法变换，在满射或双向保持的条件下，证明其为对角矩阵乘法、置换矩阵乘法、转置及基域单射自同态的复合。
AI 中文摘要
矩阵$A$的永久秩是其非零永久值的最大平方子矩阵的阶数。本文刻画了保持永久秩1矩阵的加法变换$\boldsymbol{\u03a6}$。在$\boldsymbol{\u03a6}$为满射或双向保持永久秩1的附加假设下，证明$\boldsymbol{\u03a6}$是与对角矩阵、两侧置换矩阵的乘法、转置及基域的单射自同态的复合。
英文摘要
The permanent rank of a matrix $A$ is the size of the maximal square submatrix in $A$ which has a nonzero permanent. In this paper we characterize additive transformations $Φ$ which preserve matrices of per-rank-one. Under an additional assumption that $Φ$ is surjective or that it preserves per-rank-one in both directions we prove that $Φ$ is a composition of a multiplication with diagonal matrices and permutation matrices from both sides, transposition, and injective endomorphism of the base field.
